Detroit had chances against Hart, but puck luck wasn't in the cards for the Wings, who missed on several opportunities, especially on well-executed backdoor plays.
But in the end, Hart was terrific, making 37 saves and showing mental toughness after having a bit of a meltdown in the third period Saturday when the Wings scored four consecutive goals to knot the score at 5-5.
Darren Helm scored the Wings' goal, while Oskar Lindblom netted two (one empty net) for Philadelphia, with Ivan Provorov notching the game winner early in the third period for the Flyers.
Detroit goaltender Jimmy Howard, who replaced Jonathan Bernier after the first period due to injury, had 11 saves.
With the loss, the Red Wings drop to 23-29-8 on the seaspm, while the Flyers improved to 28-24-7.
Up next, the Wings will host their former Central Division rival, the Chicago Blackhawks, on Wednesday, in the second game of their current five-game homestand.
Philadelphia returns to action on Tuesday when it welcomes the league-leading Tampa Bay Lightning to the Wells Fargo Center.
1. Anthony Mantha: With about five minutes left in the third period of Saturday afternoon's game in Philadelphia, Mantha cross-checked Flyers captain Claude Giroux along the boards. Flyers fans were incensed when there was no call. But Mantha knew retribution was coming and it came early in Sunday's game in Detroit. Just 53 seconds into the game, Wayne Simmonds challenged Mantha and the two had a brief bout. The battle appeared to spark Mantha, who led all skaters with seven shots. Mantha, who scored twice to help the Wings rally to force overtime in Philly, did not score at home Sunday but had plenty of chances. Mantha finished with 17 shifts for 18:51, had the seven shots, three hits, one takeaway, was 1-for-1 in face-offs and was minus-2.
Quotable: "Obviously I didn't want to, I'll be honest. But I step up for myself. The hit was kind of a weird hit yesterday. I knew I was gonna need to step up. He told me right before the anthem he wanted me, so I said, 'Let's get it over with,' and play some hockey. Obviously he's a tough customer. I did watch a couple of clips. He always switches to lefty, so I was trying to hold on to that left. The hand did come in mind. I guess the doctor did a great job." -- Mantha